The mutual has reportedly hired Buckingham Corporate Finance to handle the sale of Sunwin Services, which could raise £30m or £40m.
Sunwin provides secure transport of cash for stores and dispensers, as well as security, fire detection and IT services.
Co-op chief executive Peter Marks (pictured) has previously spoken of the need for “scale” but that does not mean he will sell the smaller businesses within the group.
The sale of Lloyds’ Verde assets would create Britain’s seventh-biggest bank. Yesterday a Co-op spokesman declined to comment on “speculation”. More information could emerge on Thursday, however, when the group publishes its full-year results.